New topological rainbow trapping approach for phononic beam-foundation systems

Rainbow trapping is of great significance for frequency-based wave splitting and broadband wave attenuation. By recognizing the deficiency of prevailing gradient rainbow reflection devices in terms of energy concentration and broadband vibration isolation, we design a new topological rainbow trapping device by introducing a topological protected interface mode (TPIM) into the prevailing gradient rainbow device. Therefore, a topological rainbow trapping beam composed of a homogenous beam rested on an alternate and gradient foundation is constructed. Using theoretical and numerical analysis, we perform a unit-cell band structure analysis. The dependence of bandgap region and group velocity on the reference foundation stiffness is investigated. With the help of the topological phase transition and Zak phase analysis, we successfully predict and demonstrate TPIM. A quantitative evaluation of the advancement of topological rainbow devices upon the prevailing gradient device in vibration amplification and broadband wave attenuation is also presented. We believe that the robust one-dimensional topological rainbow trapping beam will be useful in many applications, such as energy harvesting, wave splitting, and vibration control.